Quite the opposite actually, if you're a citizen of it you have some constitutional protection against your own government spying on you, at least in the U.S. AFAIK. If you are outside of it, you're fair game.
In theory i agree if you read up on what is shared about it.
In practice i have very strong doubts this is a fact. Specially since there is '5 eyes', '6 eyes', '9 eyes' and '14 eyes'. And any of the members are monitoring domestic terrorism, so i fail to see how they are not spying on their own citizens.
